A complete ranking of incomplete trapezoidal information

Nayagam, V. Lakshmana Gomathi; Ponnialagan, Dhanasekaran; Jeevaraj, S.

doi:10.3233/ifs-152064

Cited by 13 publications

(3 citation statements)

References 17 publications

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“…However, unfortunately, every time, the available methods have some drawbacks, which are rectified by the new method, which is where the research gap exists [10]. Total ordering on the set of intuitionistic fuzzy numbers has been achieved by a few researchers [12], [13]. Peng and Yang [15] introduce the idea of score and accuracy function on the set of IVPFNs to compare arbitrary IVPFNs.…”

Section: Introductionmentioning

confidence: 99%

Membership Score of an Interval-Valued Pythagorean Fuzzy Numbers and Its Applications

Alrasheedi

Jeevaraj

2023

IEEE Access

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The main aim of the paper is to define a new Membership score function on the class of interval-valued Pythagorean fuzzy numbers which can overcome the drawbacks of existing familiar ranking methods. In this paper, firstly, we show the limitations of various ranking functions in ordering/ comparing any two arbitrary interval-valued Pythagorean fuzzy numbers in detail. Secondly, we define a new Membership score function on the class of interval-valued Pythagorean fuzzy numbers and study their properties. Then we compare our proposed method with many other different existing methods for showing the efficacy of the proposed method. Finally, we show the applicability of the proposed Membership score function in solving interval-valued Pythagorean fuzzy multi-criteria decision-making problems using a numerical example. INDEX TERMS Interval-valued Pythagorean fuzzy numbers, improved accuracy score function, membership score function, MCDM.

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Section: Introductionmentioning

confidence: 99%

Membership Score of an Interval-Valued Pythagorean Fuzzy Numbers and Its Applications

Alrasheedi

Jeevaraj

2023

IEEE Access

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“…If the problem is modelled using TrIFNs, it is necessary to study the ranking principle to compare arbitrary TrIFNs. The ranking of TrIFNs [4,5] plays a vital role in solving problems modelled using trapezoidal intuitionistic fuzzy numbers. Researchers worldwide have introduced various ranking principles for comparing two arbitrary trapezoidal intuitionistic fuzzy numbers.…”

Section: Introductionmentioning

confidence: 99%

Trapezoidal Intuitionistic Fuzzy Power Heronian Aggregation Operator and Its Applications to Multiple-Attribute Group Decision-Making

Jeevaraj

Gatiyala

Zolfani

2022

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Decision-making problems involve imprecise and incomplete information that can be modelled well using intuitionistic fuzzy numbers (IFNs). Various IFNs are available in the literature for modelling such problems. However, trapezoidal intuitionistic fuzzy numbers (TrIFNs) are widely used. It is mainly because of the flexibility in capturing the incompleteness that occurs in the data. Aggregation operators play a vital role in real-life decision-making problems (modelled under an intuitionistic fuzzy environment). Different aggregation operators are available in the literature for better decision-making. Various aggregation operators are introduced in the literature as a generalization to the conventional aggregation functions defined on the set of real numbers. Each aggregation operator has a specific purpose in solving the problems effectively. In recent years, the power average (PA) operator has been used to reduce the effect of biased data provided by decision-makers. Similarly, the Heronian mean (HM) operator has a property that considers the inter-relationship among various criteria available in the decision-making problem. In this paper, we have considered both the operators (HM, PA) to introduce a new aggregation operator (on the set of TrIFNs), which takes advantage of both properties of these operators. In this study, firstly, we propose the idea of a trapezoidal intuitionistic fuzzy power Heronian aggregation (TrIFPHA) operator and a trapezoidal intuitionistic fuzzy power weighted Heronian aggregation (TrIFPWHA) operator by combining the idea of the Heronian mean operator and power average operator in real numbers. Secondly, we study different mathematical properties of the proposed aggregation operators by establishing a few essential theorems. Thirdly, we discuss a group decision-making algorithm for solving problems modelled under a trapezoidal intuitionistic fuzzy environment. Finally, we show the applicability of the group decision-making algorithm by solving a numerical case problem, and we compare the proposed method’s results with existing methods.

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“…Further, it has been generalized to various forms such as intuitionistic fuzzy numbers, Pythagorean fuzzy numbers, Fermatean fuzzy numbers, Bipolar fuzzy numbers, etc. Various ranking procedures are available on the different classes of fuzzy and intuitionistic fuzzy numbers [1,2,3,5,6,7,8,9,10,11]. Bipolar fuzzy numbers are very much valuable for modelling problems with imprecise and incomplete information.…”

Section: Introductionmentioning

confidence: 99%

Ranking of Trapezoidal Bipolar Fuzzy Numbers Based on a New Improved Score Function

Jeevaraj¹

2021

Frontiers in Artificial Intelligence and Applications

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Bipolar fuzzy numbers plays a vital role in any Decision-making problem modelled under a bipolar fuzzy environment. In 2018, Akram and Arshad [1] introduced a new ranking function on the class of Trapezoidal Bipolar fuzzy numbers based on the area of the left and right membership function of a TrBFN, and they have discriminated any two TrBFNs by using it. The ranking principle introduced by Akram and Arshad [1] works better only when two bipolar fuzzy numbers have different rankings. We describe that the ranking function does not work with counterexamples when two or more bipolar fuzzy numbers have the same rankings. In this paper, we improve the ranking principle introduced in [1] by introducing a new Improved Score function. Firstly, we discuss the drawbacks and limitations of the ranking function introduced by Akram and Arshad [1]. Secondly, we introduce a new ranking function and study its properties. Thirdly, we introduce a new ranking principle by combining Akram and Arshad’s [1] ranking function and the proposed ranking function. Finally, we show the efficiency of the proposed ranking principle in comparing arbitrary TrBFNs.

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A complete ranking of incomplete trapezoidal information

Cited by 13 publications

References 17 publications

Membership Score of an Interval-Valued Pythagorean Fuzzy Numbers and Its Applications

Membership Score of an Interval-Valued Pythagorean Fuzzy Numbers and Its Applications

Trapezoidal Intuitionistic Fuzzy Power Heronian Aggregation Operator and Its Applications to Multiple-Attribute Group Decision-Making

Ranking of Trapezoidal Bipolar Fuzzy Numbers Based on a New Improved Score Function

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